Trans-Lunar Trajectory Correction Maneuver – OTB

Optimize a single impulsive trajectory correction maneuver (TCM) located on a trans-lunar trajectory.

This is a MATLAB script named translunar_tcm_otb that can be used to optimize a single trajectory correction maneuver (TCM) at a user-defined time and geocentric state vector (position and velocity vectors) on a trans-lunar (Earth-to-Moon) trajectory. This TCM can be used to correct trajectory dispersions or perhaps re-target a lunar free return trajectory to different selenocentric final mission conditions.

The software assumes the TCM occurs impulsively which results in a discontinuity in the geocentric velocity vector but not the position vector.

The type of final selenocentric (Moon-centered) mission constraints can be selected by the user from one of the following script options;

1. selenocentric radius and inclination
2. selenocentric user-defined b dot r and b dot t
3. selenocentric node/apse alignment

The characteristics of the final selenocentric mission constraints can be calculated in one of the following three different coordinate systems;

1. Earth true-of-date
2. Earth mean equator and equinox of J2000
3. mean lunar equator and IAU node of epoch).

In the translunar_tcm_otb “simple shooting” algorithm, the spacecraft orbital motion includes the Earth’s non-spherical gravity and the point-mass perturbations of the Sun and Moon.

This MATLAB script reads JPL DE430 lunar and solar ephemerides in a machine-independent binary format (kernels) which are available from the SPICE web site and by anonymous ftp from ftp://ssd.jpl.nasa.gov/pub/eph/planets/bsp. These *.bsp ephemeris files are IEEE-Little Endian style of binary kernel. This is the binary form native to PC/Linux, PC/Windows and MAC/Intel machines. Additional information about JPL ephemerides can be found at http://naif.jpl.nasa.gov/naif/.

The translunar_tcm_otb script uses routines from the MICE software suite to read and evaluate the JPL ephemeris file. Platform-specific MICE mex files, support functions and the binary ephemeris file (de430.bsp) are available at naif.jpl.nasa.gov/naif/toolkit_MATLAB.html. MICE is a MATLAB implementation of the SPICE library created by JPL.

This MATLAB script uses the fmincon (minimization with constraints) algorithm of the Mathworks® Optimization Toolbox to solve this optimization problem. The actual numerical method is the ‘interior-point’ algorithm.